There was little to separate the sides before the interval in Durban and were level at 6-6 as Owen Farrell and Morne Steyn traded penalties but South Africa broke down England after half-time and tries from Steyn and Jean de Villiers gave the Springboks first blood in the three-Test series.
"We went in 6-6 at half-time, we came out all guns blazing but unfortunately they got an early score and managed to build pressure on us," captain Robshaw told Sky Sports 2.
"South African sides, you always know they're going to be very physical but if you looking at the game we were never more than a score away but unfortunately we were the wrong side of that score.
"We have to start building for next week, there's been a lot of positives and a couple negatives you can pick out today."
Ben Foden's try was mere consolation but was reward for England's endeavour in the closing stages and Robshaw hopes they can take that into next Saturday's clash.
"In this three-match series of course we would have liked to have won the first match but it's onwards and upwards now and there's a lot of hard work to do.
"It's all about the result at the end of the day but the last 10-15 minutes we showed we can put our game on the pitch and move them around.
"We did that
throughout the majority of the first half but we've got to start to do it for the full 80 minutes."
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